Recombination groups in database{ …_zb{} } and database{ …_wz{} }

There are about 23 identical groups available directly under all zincblende- and wurtzite-related groups. In this section we describe one of them, specifically the group related to recombination models recombination{}.

database{ …{ recombination{} } }

This section specifies the coefficients related to recombination processes. These are used when the current equation is solved. In nextnano++, the following recombination processes are included:

• Shockley-Read-Hall (SRH) recombination

• Auger recombination

• Radiative recombination

Example

binary_zb {
    name    = Si                        # material name, e.g. Si, GaAs, InP, ...

        ...

    recombination{
                                        # Shockley-Read-Hall recombination
        SRH{        tau_n  = 1.0e-9     # [s]    zero doping scattering time for electrons
                    nref_n = 1.0e19     # [cm^-3] reference doping concentration for electrons
                    tau_p  = 1.0e-9     # [s]    zero doping scattering time for holes
                    nref_p = 1.0e18     # [cm^-3] reference doping concentration for holes
        }

                                        # Auger recombination
        Auger{      c_n    = 2.8e-31    # [cm^6/s]
                    c_p    = 9.9e-31    # [cm^6/s]
        }

                                        # direct recombination
        radiative{  c = = 2.0e-10   }   # [cm^3/s]
                                        # 2.0e-10 for GaAs, 0 for Si (indirect semiconductor)

    }

}

Shockley-Read-Hall (SRH) recombination

SRH model models the generation/recombination process that is assisted by impurities. The recombination/generation rates depend on the deviation of the carrier concentration from the equilibrium value and the scattering rates depend on the doping concentration. The rate is calculated using the following formulas:

$$\begin{array}{r}\begin{array}{rl}{R}_{SRH}& =\frac{p\cdot n-n_i^2}{{\tau }_p(n+n_i)+{\tau }_n(p+p_i)},\\ {\tau }_{p/n}& =\frac{{\tau }_{p0/n0}}{1+\frac{N_D+N_A}{N_n/p,ref}},\end{array}\end{array}$$

where ${\tau }_{n0}$ is zero doping scattering time for electrons, $N_{n,ref}$ is reference doping concentration for electrons, ${\tau }_{p0}$ is zero doping scattering time for holes, and $N_{p,ref}$ is reference doping concentration for holes.

tau_n

zero doping scattering time for electrons ${\tau }_{n0}$

type:

double

unit:

s

nref_n

reference doping concentration for electrons $N_{n,ref}$

type:

double

unit:

cm^-3

tau_p

zero doping scattering time for holes ${\tau }_{p0}$

type:

double

unit:

s

nref_p

reference doping concentration for holes and $N_{p,ref}$

type:

double

unit:

cm^-3

Auger recombination

More imformation on physics: Auger recombination processes in semiconductor heterostructures.

Auger process is a dominant recombination channel for devices with an extremely high carrier concentrations. It is a three-particle process, therefore, scaling with the third power of the carrier density.

The phonon-assisted Auger recombination rate, which plays an important role especially at high carrier injection, is modeled by the following equation:

$$R_{Auger}=(C_{n}n+C_{p}p)\cdot (np-n_i^2),$$

where $C_n$ and $C_p$ are coefficients.

c_n

coefficient $C_n$

type:

double

unit:

cm⁶ s^-1

c_p

coefficient $C_p$

type:

double

unit:

cm⁶ s^-1

More imformation on physics: Auger recombination processes in semiconductor heterostructures.

Radiative recombination

The simplest, and the most important for light emitting devices, process for the generation and recombination of electron-hole pairs is the direct emission or absorption spectra of a photon (radiative recombination) modelled within the formula

$$R_{radiative}=C(np-n_i^2),$$

where $C$ is a coefficient.

c

a coefficient $C$

type:

double

unit:

cm³ s^-1

example:

2.0e-10 (for GaAs), 0.0 (for Si, indirect semiconductor)

c_absorption

If c_absorption > c, then c_absorption will be used instead of c as $C$ to compute absorption coefficients in semiclassical optics. This can be used to enable and control absorption for indirect bandgap materials where c practically vanishes. Ideally, for these materials, c_absorption should be set in the database to values which reproduce the experimentally observed absorption coefficients.

type:

double

unit:

cm³ s^-1

default:

1e-11